Stopping a character fall in Blender Game Engine
The way you implemented a solution is that the object has no gravity.

This is not really the behavior of an object that "holds on another object" (character holding at the ladder).

You currently discover "an area without gravity". That means when the character jumps into that area it will preserve it's motion and direction (while gravity would would do the same but adds another force influencing motion and direction).

I suggest you implement a "holding" onto the ladder, e.g. by parenting the object to the ladder [or any other way to restrict the position to the holding point].

While holding any previously active controls (like jumping, walking crouching) will not work anymore as the character is not a freely moving physics object. This is fine, because your character holds itself to the ladder.

You need other "operations" like move up/down (but not via linear velocity and such things).
Additional you should implement a "release operation" that let the character release the grip returning to the normal behavior (incl. falling).

Other operations could benefit from release too - you can combine jump and release. I suggest to first release and jump afterwards. Otherwise the exiting "hold" would disable the jump.

What problems could happen?

A) Parenting is a hard attachment. This means when you throw the ladder around, the character will not care and still hold onto it. If you really need such situations, you could release the character before (or while) moving the ladder.

B) The character ignores collisions while moving on the ladder. While parented the physics has no influence. Unfortunately there is not much you can do here, except sensing for such collisions and acting accordingly. E.g. you sense if there is a blocking object above the character before allowing the "move up" operation.

I hope this helps a bit.